of the compressor can be both negative around refractive index n = 1.6 (red curve) and positive (blue curve). The range with a negative dispersion is relatively short since prism P2 can only be moved upwards over a short distance before the light ray misses it altogether. In principle, the α angle can be varied to tune the dispersion properties of a prism compressor. In practice, however, the geometry is chosen such that the incident and refracted beam have the same angle at the central wavelength of the spectrum to be compressed. This configuration is known as the "angle of minimum deviation", and is easier to align than arbitrary angles. The refractive index of typical materials such as BK7 glass changes only a small amount (0.01 – 0.02) within the few tens of nanometers that are covered by an ultrashort pulse. Within a practical size, a prism compressor can only compensate a few hundred μm of path length differences between the wavelength components. However, by using a large refractive index material (such as SF10, SF11, etc.) the compensation distance can be extended to mm level. This technology has been used successfully inside femtosecond laser cavity for compensation of the Ti:sapphire crystal, and outside for the compensation of dispersion introduced by other elements. However, high-order dispersion will be introduced by the prism compressor itself, as well as other optical elements. It can be corrected with careful measurement of the ultrashort pulse and compensate the phase distortion. MIIPS is one of the pulse shaping techniques which can measure and compensate high-order dispersion automatically. As a muddled version of pulse shaping the end mirror is sometimes tilted or even deformed, accepting that the rays do not travel back the same path or become divergent. Dispersion theory The angular dispersion for generalized prismatic arrays, applicable to laser pulse compression, can be calculated exactly using the multiple-prism dispersion theory. In particular, the dispersion, its first derivative, and its second derivative, are given by where Angular quantities are defined in the article for the multiple-prism dispersion theory and higher derivatives are given by Duarte. Comparison with other pulse compressors The most common other pulse compressor is based on gratings (see Chirped pulse amplification), which can easily create a much larger negative dispersion than a prism compressor (centimeters rather than tenths of millimeters). However, a grating compressor has losses of at least 30% due to higher-order diffraction